Two-dimensional gravity with an invariant energy scale and arbitrary dilaton potential

We investigate a model of two-dimensional gravity with arbitrary scalar potential obtained by gauging a deformation of de Sitter or more general algebras, which accounts for the existence of an invariant energy scale. We obtain explicit solutions of the field equations and discuss their properties.Comment: 8 pages, LaTe

Classical and quantum mechanics of the nonrelativistic Snyder model in curved space

The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales besides the speed of light, and is invariant under the action of the de Sitter group. Here we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS). By means of a nonlinear transformation relating the SdS phase space variables to canonical ones, we are able to investigate the classical and the quantum mechanics of a free particle and of an oscillator in this framework. As in their flat space limit, the SdS and aSdS models exhibit rather different properties. In the SdS case, a lower bound on the localization in position and momentum space arises, which is not present in the aSdS model. In the aSdS case, instead, a specific combination of position and momentum coordinates cannot exceed a constant value. We explicitly solve the classical and the quantum equations for the motion of the free particle and of the harmonic oscillator. In both the SdS and aSdS cases, the frequency of the harmonic oscillator acquires a dependence on the energy.Comment: 21 pages; discussion of three-dimensional quantum mechanics added, error in quantum commutators correcte

Hamiltonian formalism and spacetime symmetries in generic DSR models

We study the structure of the phase space of generic models of deformed special relativity that gives rise to a definition of velocity consistent with the deformed Lorentz symmetry. As a byproduct we also determine the laws of transformation of spacetime coordinates.Comment: 10 pages TeX; v.2 completely rewritten; v.4 some typos corrected and some points clarifie

Dyonic black holes in effective string theories

The spherical symmetric dyonic black hole solutions of the effective action of heterotic string are studied perturbatively up to second order in the inverse string tension. An expression for the temperature in term of the mass and the electric and magnetic charge of the black hole is derived and it is shown that its behaviour is qualitatively different in the two special cases where either the electric or the magnetic charge vanishesComment: 8 page